Finite Group Databasebeta

← #15757901

Subgroups — #15757901

Order 3328.

558 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123877C211yesmaximal, characteristic
2#13118095C211yesmaximal, characteristic
3#13114936C212yesmaximal, complemented
4#13112722C212yesmaximal, complemented
5C4×C13×#99C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88180C2211yescharacteristic
8C2×C13×#99—21no—
9C4×C13×C22⋊C4C2212yes—
10#11718883—21no—
11C4×C22⋊Dic13—21no—
12C4×C22⋊Dic13C2211yescharacteristic
13#11718868—21no—
14#11718868C2212yes—
15#11718673—24no—
16#11718647C411yescharacteristic, complemented
17#11718644C411yescharacteristic, complemented
18#11718614C411yescharacteristic, complemented
19#11718613—21no—
20#11718610C411yescharacteristic, complemented
21C4×#6101—21no—
22#11718586—21no—
23C13×#342—21no—
24#11718115—24no—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13—22no—
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40#88180—22no—
41#88180—22no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13—21no—
48C2×#6099—22no—
49C2×#6099D414yes—
50C13×#99—24no—
51C13×#95—22no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic
57#88071C2×C411yescharacteristic
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055—22no—
61C4⋊#1055—22no—
62C4×#1055—22no—
63#9012—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13#4112yes—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C13×C4⋊C4—22no—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—42no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—44no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C4⋊Dic13—22no—
98C4⋊Dic13—22no—
99#6101—42no—
100#6101—42no—
101C4×Dic13—42no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104#6099—44no—
105#6099—82no—
106C2×#1055—24no—
107#2975—131no—
108#2395—131no—
109#1826—132no—
110C4×#99D1311yescharacteristic
111#1297—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13#12112yes—
123D4×C13—44no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—24no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—44no—
136C2×C4×C13—81no—
137C2×C4×C13—82no—
138C2×C4×C13—82no—
139C2×C4×C13#10412yes—
140C2×C4×C13C4×D412yes—
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×Dic13—22no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155#1055—44no—
156C2×C4×D4C2×D1311yescharacteristic
157C2×#117—131no—
158#436—264no—
159#431—261no—
160C2×#99—21no—
161#407—132no—
162#407—261no—
163#400—131no—
164#399—131no—
165#398—131no—
166#397—131no—
167#397—261no—
168#394—261no—
169C4×C4⋊C4—261no—
170C4×C22⋊C4—131no—
171C4×C22⋊C4—261no—
172C4×C22⋊C4C2×D1312yes—
173#342—21no—
174#339—264no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—42no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13#38611yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13#42111yescharacteristic
190C4×C13—22no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—84no—
196C4×C13#45812yes—
197Dic13—42no—
198Dic13—81no—
199Dic13—81no—
200Dic13—81no—
201C22×D4C22⋊D1311yescharacteristic
202C23×C4D5211yescharacteristic
203C23×C4C22×D1311yescharacteristic
204C2×M16—134no—
205C2×M16—262no—
206C4×D4—22no—
207C4×D4—22no—
208#117—262no—
209#117—262no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4C4×D1311yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4C4×D1311yescharacteristic
221C2×C22⋊C4C22⋊D1311yescharacteristic
222C2×C42—22no—
223C2×C42—261no—
224C2×C42—261no—
225C2×C42D5211yescharacteristic
226C4⋊C8—262no—
227#99—24no—
228C22⋊C8—262no—
229C22⋊C8—262no—
230C22⋊C8—262no—
231C4×C8—262no—
232#95—22no—
233#95—131no—
234#95—131no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95—261no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—42no—
242C2×C13—81no—
243C2×C13#187111yescharacteristic
244C2×C13#188411yescharacteristic
245C2×C13#189011yescharacteristic
246C24#610311yescharacteristic
247C24C2×C22⋊D1311yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4#610311yescharacteristic
261C22×C4#610311yescharacteristic
262C22×C4#610311yescharacteristic
263C22×C4C2×C4×D1311yescharacteristic
264C22×C4C2×D5211yescharacteristic
265C22×C4D4×D1312yes—
266C22×C4#612912yes—
267M16—524no—
268M16—1042no—
269C2×C8—264no—
270C4⋊C4—22no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—24no—
278C22⋊C4—42no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C42—21no—
284C42—21no—
285C42—44no—
286C42—522no—
287C42—521no—
288C42—521no—
289C13#901211yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×#610311yescharacteristic
300C23#8819312yes—
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—262no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4#8804512yes—
330C2×C4#8813512yes—
331C2×C4#8813611yescharacteristic
332C2×C4#8814011yescharacteristic
333C8—524no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22C2×#8804511yescharacteristic
347C22#1171861911yescharacteristic
348C22#1171866611yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—84no—
355C4—522no—
356C4—1041no—
357C4—1041no—
358C4—1041no—
359C4#1171840312yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1311513611yescharacteristic
365C2#1311521711yescharacteristic
366C2#1311524711yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC4×C13×#99C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenterC4×#99D13
hypocenterC13#9012
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13114936C2semidirect
4. #13112722C2semidirect
16. #11718647C4semidirect
17. #11718644C4semidirect
18. #11718614C4semidirect
20. #11718610C4semidirect
289. C13#9012semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131238772
#131180952
#131149362
#131127222
C4×C13×#992
#901213